Langevin Monte Carlo
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Related Articles from SNS
Generalization of Gibbs and Langevin Monte Carlo Algorithms in the Interpolation Regime
Announce Type: replace Abstract: This paper provides data-dependent bounds on the expected error of the Gibbs algorithm in the overparameterized interpolation regime, where low training errors are also obtained for impossible data, such as random labels in classification. The results show that generalization in the low-temperature regime is already signaled by small training errors in the noisier high-temperature regime. The bounds are stable under approximation with Langevin Monte Carlo...
Improved Guarantees for Langevin Monte Carlo with Average Smoothness
arXiv:2605.31413v1 Announce Type: cross Abstract: We establish improved nonasymptotic bounds for Langevin Monte Carlo in the strongly log-concave setting, when the error is measured by the Wasserstein distance. The main result shows that the discretization error is governed by an average coordinate-wise smoothness constant, rather than by the usual global smoothness constant. The proof is short and probabilistic, and relies on a refined use of the synchronous coupling.
Local and Global Contraction Principles for MCMC Mixing
arXiv:2606.03033v1 Announce Type: new Abstract: We develop a contraction-based framework for proving mixing-time bounds for Markov chain Monte Carlo algorithms. The framework is built around global and local contraction coefficients of Markov kernels under the $\mathsf E_\gamma$-divergence with $\gamma\ge1$. For projected Langevin Monte Carlo on a compact convex domain, we show that Gaussian smoothing yields an explicit global contraction coefficient for the $\mathsf E_\gamma$-divergence....